2 00 4 Calculation of mixed Hodge structures , Gauss - Manin connections and Picard - Fuchs equations


In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension n in terms of differential forms. In the case n = 1 such computations have many applications in differential equations and counting their limit cycles. For n > 3… (More)